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We introduce a versatile bottom-up derivation of a formal theoretical framework to describe (passive) soft-matter systems out of equilibrium subject to fluctuations.We provide a unique connection between the constituent-particle dynamics of real systems and the time evolution equation of their measurable (coarse-grained) quantities, such as local density and velocity. The starting point is the full Hamiltonian description of a system of colloidal particles immersed in a fluid of identical bath particles. Then,we average out the bath viaZwanzig’s projection-operator techniques and obtain the stochastic Langevin equations governing the colloidal-particle dynamics. Introducing the appropriate definition of the local number and momentum density fields yields a generalisation of the Dean–Kawasaki (DK) model, which resembles the stochastic Navier–Stokes description of a fluid.Nevertheless, the DK equation still contains all the microscopic information and, for that reason, does not represent the dynamical law of observable quantities.We address this controversial feature of the DK description by carrying out a nonequilibrium ensemble average. Adopting a natural decomposition into local-equilibrium and nonequilibrium contribution,where the former is related to a generalised version of the canonical distribution,we finally obtain the fluctuating-hydrodynamic equation governing the time-evolution of themesoscopic density and momentum fields.Along the way,we outline the connection between the ad hoc energy functional introduced in previous DK derivations and the free-energy functional from classical density-functional theory.The resultant equation has the structure of a dynamical density functional theory (DDFT) with an additional fluctuating force coming from the random interactions with the bath.We show that our fluctuating DDFT formalism corresponds to a particular version of the fluctuating Navier–Stokes equations, originally derived by Landau and Lifshitz. Our framework thus provides the formal apparatus for ab initio derivations of fluctuating DDFT equations capable of describing the dynamics of soft-matter systems in and out of equilibrium. [ABSTRACT FROM AUTHOR]

Transcription elongation rates influence RNA processing, but sequence-specific regulation is poorly understood. We addressed this in vivo , analyzing RNAPI in S. cerevisiae. Mapping RNAPI by Miller chromatin spreads or UV crosslinking revealed 5′ enrichment and strikingly uneven local polymerase occupancy along the rDNA, indicating substantial variation in transcription speed. Two features of the nascent transcript correlated with RNAPI distribution: folding energy and GC content in the transcription bubble. In vitro experiments confirmed that strong RNA structures close to the polymerase promote forward translocation and limit backtracking, whereas high GC in the transcription bubble slows elongation. A mathematical model for RNAPI elongation confirmed the importance of nascent RNA folding in transcription. RNAPI from S. pombe was similarly sensitive to transcript folding, as were S. cerevisiae RNAPII and RNAPIII. For RNAPII, unstructured RNA, which favors slowed elongation, was associated with faster cotranscriptional splicing and proximal splice site use, indicating regulatory significance for transcript folding. • Structures in the nascent RNA correlate with rapid elongation by RNAPI in vivo • Stable RNA structures limit RNAPI backtracking in vitro • GC content in the transcription bubble tunes transcription elongation rate • Nascent transcript folding modulates dynamics of all three RNAPs in vivo Transcription elongation is a stochastic process that can go backward as well as forward. Here Turowski et al. report that folding of the nascent transcript immediately behind the polymerase resists backtracking and promotes forward movement. This results in faster elongation relative to unstructured sequences and is potentially important for cotranscriptional processing. [ABSTRACT FROM AUTHOR]